As far as we know, there are no theoretical results for estimators that necessarily interpolate in the model (REF ) when \(\mathcal {O} \ne \emptyset \) . In the noiseless case where \(\mathcal {O}=\emptyset \) ,
[1]} have proposed and investigated an interpolating estimator, similarly defined as (REF ) with the minimum replaced by an average and an additional matching sign constraint. In particular, they showed that this estimator is able to consistently estimate the direction of \(\beta ^*\) .
